1 Math Circle WARM UP Questions to consider: Please rank the following events. Make your best guess as to what happened when. Moon Landing Apollo 13 Invention of the pocket calculator Invention of the slide rule Invention of the first central processing unit (CPU)/ Computer. Graphing Calculators. iphone Invention of Calculus John Napier First Manned Shuttle in Space First Woman in Space
2 Building the Scale of Multiplication Lines 2.1 Building the Addition Table Starting with a given column and adding the given row value, build an addition table. What patterns do you see? 2.2 Building the Multiplication Table 10 9 8 7 6 5 4 3 2 1 0 + 0 1 2 3 4 5 6 7 8 9 10 Starting with a given column and multiplying the given row value, build a multiplication table. What patterns do you see? 10 10 20 30 40 50 60 70 80 90 100 9 9 18 27 36 45 54 63 72 81 90 8 8 16 24 32 40 48 56 64 72 80 7 7 14 21 28 35 42 49 56 63 70 6 5 4 3 2 1 x 1 2 3 4 5 6 7 8 9 10
3 Making Our Own Sliding Scale 1. Start with a ruler: 2. Let s create a multiplication scale, a gradation of the ruler at regular intervals that we can use to multiply. Given this ruler add numbers to create a scale. Questions to consider: What number do you start with? hint: where does the multiplication chart start with? How far between di erent integers? If you ve placed 2 and 4, where does 3 go? Is it closer to 2, closer to 4, or equal? Where is 10? Where is 100? How do you read numbers that are o the scale? 3. Let s stack 2 scales on top of each other and shift the top so that the first gradation on top is on top of the 2nd gradation of the bottom scale. C D I II III IV V VI Question: How does the top scale compare to the bottom scale for a given gradation? 4. Let s stack 2 scales on top of each other and shift the top so that the first gradation on top is on top of the 3nd gradation of the bottom scale. C D I II III IV V VI Question: How does the top scale compare to the bottom scale for a given gradation?
Virtual Pickett N600-ES Slide Rule 4 http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html Reading the Slide Rule Images from http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html Virtual Pickett N600-ES Slide Rule http://www.antiquark.com/sliderule/sim/virtual-slide-rule.h Virtual Pickett N600-ES Slide Rule http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html 1 of 1 1/23/12 2:35 PM
Virtual Pickett N600-ES Slide Rule http://www.antiquark.com/sliderule/sim/virtual-slide-rule.html 5 Somethings to Consider with Slide Rule Calculations 1. What is the largest multiplication you can calculate? 2. What is the most accuracy that you can obtain with slide rules? 3. How much accuracy do you need with a slide rule? 4. How are A/B related to C/D? 5. How is K related to D? 6. How is C1 related to C? 1 of 1 1/23/12 2:37 PM
6 Slide Rule Calculations 1. 1.2 x 3.6 = 2. 2 x 3.6 = 3. 1.7 x 3.6 = 4. Draw 2 slides and show how you line them us to calculate xy (x multiplied by y): 5. 3 / 1.5 = 6. 3.6 / 4.2 = 7. Draw 2 slides and show how you line them us to calculate x/y (x divided by y): 8. 4.2 x 6.7 = 9. Question: What do you do when you run out of slide? Draw the slides for another process: 10. 1 2 11. 3 2 12. 6.2 2 = 13. 3.6 2 x4.3 2 = 14. Draw 2 slides and show how you line them us to calculate x 2 (x squared) 15. p 24 16. p 67 17. Draw 2 slides and show how you line them us to calculate p x (square root of x ) 18. p 45 p 36= 19. Log(1) 20. Log(6) 7 Additional Resources http://www.sliderulemuseum.com/ International Slide Rule Museum: http://www.sliderulemuseum.com/ Slide Rule Course http://sliderulemuseum.com/sr_loaner.htm Slide Rule Loaner Program http://www.youtube.com/watch?v=zmv_r2honni&feature=related - Building the multiplication Table http://www.hpmuseum.org/sliderul.htm - HP Museum Slide Rule Article http://jamiecolliemathematics.blogspot.com/2010/12/test-955.html Logarithms: Much More Than Just a Button on the Calculator! http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html Virtual Pickett Slide Rule http://www.tcf.ua.edu/az/ithistoryoutline.htm History of Calculations